Spectra of the neighbourhood corona of two graphs

Abstract

Given simple graphs (Formula presented.) and (Formula presented.) , the neighbourhood corona of (Formula presented.) and (Formula presented.) , denoted (Formula presented.) , is the graph obtained by taking one copy of (Formula presented.) and (Formula presented.) copies of (Formula presented.) , and joining the neighbours of the (Formula presented.) th vertex of (Formula presented.) to every vertex in the (Formula presented.) th copy of (Formula presented.). In this paper we determine the adjacency spectrum of (Formula presented.) for arbitrary (Formula presented.) and (Formula presented.) , and the Laplacian spectrum and signless Laplacian spectrum of (Formula presented.) for regular (Form..